The basic relationships for parameters such as removal rate, power, and grinding conditions are not in every case the same as for grinding between centers. The basic relationships for centerless grinding are as follows.
19.3.1 Depth of Cut
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The real depth of cut at the commencement of grinding is less than expected because of machine and system deflections. With uniform infeed, depth of cut and deflections build up to a steady value. The steady value of real depth of cut is
where vf is the infeed rate, nw is the work rotational speed, dw is the work diameter, and vw is the workspeed.
It is important to include the factor of one half. This factor arises because feed is relative to the workpiece diameter. As the workpiece diameter reduces, the workpiece center retreats from the grinding wheel so that the depth of cut is halved. The depth of cut is necessary for determination of removal rate.
19.3.2 Removal Rate
The rate material is removed from the workpiece is given by
Q = a ■ b ■ v (19.8)
It is more useful when assessing the overall efficiency of material removal to consider specific removal rate. Specific removal rate is the removal rate per unit width of contact of the grinding wheel.
Ql = Qbw (19.9)
19.3.3 Power
In many cases, power can be measured directly from the machine. If there is provision for measurement of tangential grinding force on a machine, power can be derived from
P = Ft ■ v (19.10)
where Ft is tangential grinding force and vs is the grinding speed.